Encoder Embedding for General Graph and Node Classification

TL;DR

This paper extends graph encoder embedding techniques to general graph models, including weighted and kernel graphs, providing theoretical guarantees and demonstrating effectiveness across various data types.

Contribution

It introduces a generalized encoder embedding method with proven statistical properties and validates its performance on diverse graph-based data.

Findings

Encoder embedding satisfies law of large numbers and CLT per observation.

Achieves asymptotic normality per class under certain conditions.

Effective on weighted, text, and image-derived graph data.

Abstract

Graph encoder embedding, a recent technique for graph data, offers speed and scalability in producing vertex-level representations from binary graphs. In this paper, we extend the applicability of this method to a general graph model, which includes weighted graphs, distance matrices, and kernel matrices. We prove that the encoder embedding satisfies the law of large numbers and the central limit theorem on a per-observation basis. Under certain condition, it achieves asymptotic normality on a per-class basis, enabling optimal classification through discriminant analysis. These theoretical findings are validated through a series of experiments involving weighted graphs, as well as text and image data transformed into general graph representations using appropriate distance metrics.